Okay, you have
that badass character ready to kick butt! Where do you start,
where do you go after that? Here it is. WARNING: this
text leaves out nothing that I know of, if you don't want some
spoilers don't read this before you try it yourself.

Vault 13 Cave:

This is where you come out of the vault ready
to kick butt and take names! Fortunately for you all the butt
you have to kick is a bunch of rats which is pretty much what you
are ready to handle right out the door. Check out that
skeleton in front of you for some stuff and then whip out your
pistol and prepare for battle.

The main thing to do in the Vault13 Cave is
to kill all the rats there for an initial experience boost, don't
be so hasty to leave as you can get halfway to the next level right
in that cave by knocking off the rats. Don't forget the stuff
on the skelton and that is about it! Don't try and get back
into the Vault as they are having "technical difficulties."

Shady Sands:

Okay, you head out of the Vault 13 Cave and
head for the only other place that you have on your map...Vault
15! Along the way there though you will find a small town
right below your path to Vault 15. Head for that and you will
find yourself in Shady Sands!

When you walk into Shady Sands you will
encounter Seth the main guard for the town. If you still have
your pistol in hand he will ask you to put it away which you should
do unless you want to get into a fight. I'll assume you don't
at this point. Talk to Seth for a little while and he will
tell you all about their problems with the Radscorpions and you can
also wring out the location of the Raider camp from him. Talk
to the Katrina the girl standing next to Seth, she will tell you
about the Vault that she came from and various other tidbits, grill
her for all the information that she has got and you will get some
experience. Next head over to the building to the southeast
and talk with Aradesh. He is the guy in the hooded robe
standing in the top corner. Aradesh will tell you about the
Radscorpion problem too and you can either ask him for money to
solve the problem or volunteer to do it out of the goodness of your
heart. You can also talk with Tandi, Aradesh's daughter
although she essentially has nothing to say to you unless your
charisma or speech skill is high then you can wring some
information about the Deathclaw and the location of Necropolis out
of her. Talk to the lady cooking food in the back and you
can compliment her on her cooking and gain one karma point (Karma
influences how people react to you in the game and is gained by
doing good deeds or lost by doing bad deeds).

Next go explore around the town, there are
several buildings that have things that you can pick up in
them. Search the bookshelves in all the buildings and you
will come up with some ammo for guns that you don't have (yet), a
length of rope and a couple of Scout Handbooks which you should use
to improve your Outdoorsman skill before heading back into the
wilderness.

Talk to Razlo the town doctor (located in the
building in the southeast corner of the main town square) and he
will tell you if you get a sample of the Radscorpion poison he can
make an antidote for it. You will have a chance to do this
later. Talk to the farmer on the other end of the town and if
you have the right combination of intelligence and speech skill you
can suggest to him that he rotate his crops for maximum production,
this will get you some experience. You might have to come
back to town later (after you have acquired more speech skill or
have a perk like Smooth Talker) to accomplish that.

The other thing to do is
to get Ian from the building north of Aradesh's home. Talk to
him for a while about things going on in the area, he will provide
the location of the Hub and Junktown, offer him a piece of the
action when he asks you for money to come with you, if he doesn't
take your offer, just try again until he does.

Once you have Ian you are ready to take out
the Radscorpions. You can talk to Seth and he will take you
to the Radscorpion caves where all you have to do is kill all the
Radscorpions and the quest is complete, pick up a few of the
Radscorpion tails on your way out to give to Razlo to make into
antivenom. Later, after you visit Vault 15 and get the
explosives (read next passage) you should come back to the
Radscorpion caves and blow up the entrance (see next passage) for
some additional experience.

Vault 15:

The other way you can destroy the
Radscorpions is to take the rope you find in Shady Sands and head
over to Vault 15. Once you arrive at Vault 15 head inside and
you will find some flares in the box on the right inside the door
to the vault. You will also find the place infested with mole
rats and other rat like creatures. These aren't much of a
problem, just wipe them out using your pistol and Ian will help
too. The elevator down to the second floor is broken so just
use the rope on the edge of the elevator shaft and then climb
down. Here you will find more rats, some ammo lying on the
floor and a locker with some goodies in it such as another length
of rope which you can use to go to the third level, some
explosives, and a leather jacket (that might be on the third level,
can't remember exactly). Proceed to the third level using the
rope that you find and if you go to the west end of the floor you
will receive some experience as you observe that you can't reach
the water chip as the cavern has collapsed in front of the command
area. The third floor has a couple of lockers on it that
contain a machine pistol which can be useful as well. Kill
all the rest of the rats for more experience and pick up the ammo
lying on the floor and then get out and head back to Shady
Sands.

When you arrive back at Shady Sands if you
haven't killed the Radscorpions already talk to Seth and get him to
take you to the Radscorpion Caves. Once there move your
cursor along the wall to the north as you enter the caves and you
should see a message telling you that the cavern looks weak in that
area. Get out your explosives that you picked up from Vault
15 and arm them for at least 30 seconds and then drop them in front
of the wall that looks weak. Make sure to get far away from
the explosives (heading towards the entrance to the caves) and when
they blow the cavern will collapse trapping the Radscorpions
inside. You get as much experience for doing this as you do
for killing the Radscorpions and blowing the entrance up after you
kill them. If you didn't get a Radscorpion tail by now, don't
worry as you will meet up with them in random encounters throughout
the desert, in fact you probably had a few as you headed over to
Vault 15. As long as you give one tail to Razlo at some
point you can still get the experience for helping him make the
antidote. Also you can give some of the antidote to the guy
that is laid out in the back (Seth's brother) of Razlo's shack for
some additional experience.

Thanks to Steve and Chris for pointing that last little bit out
to me.